Charges are placed on the vertices of a square as shown in the figure. Let $\vec{E}$ be the electric field and $V$ be the electric potential at the center. If the charges at $A$ and $B$ are interchanged with those at $D$ and $C$ respectively,then:

$A$ toy car with charge $q$ moves on a frictionless horizontal plane surface under the influence of a uniform electric field $\vec E$. Due to the force $q\vec E$,its velocity increases from $0$ to $6\, m s^{-1}$ in one second. At that instant,the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between $0$ to $3$ seconds are respectively:

Answer the following:
$(a)$ The top of the atmosphere is at about $400 \; kV$ with respect to the surface of the earth,corresponding to an electric field that decreases with altitude. Near the surface of the earth,the field is about $100 \; Vm^{-1}$. Why then do we not get an electric shock as we step out of our house into the open? (Assume the house to be a steel cage so there is no field inside!)
$(b)$ $A$ man fixes outside his house one evening a two-metre-high insulating slab carrying on its top a large aluminium sheet of area $1 \; m^2$. Will he get an electric shock if he touches the metal sheet next morning?
$(c)$ The discharging current in the atmosphere due to the small conductivity of air is known to be $1800 \; A$ on an average over the globe. Why then does the atmosphere not discharge itself completely in due course and become electrically neutral? In other words,what keeps the atmosphere charged?
$(d)$ What are the forms of energy into which the electrical energy of the atmosphere is dissipated during lightning?

Two identical charged spheres of material density $\rho$,suspended from the same point by inextensible strings of equal length,make an angle $\theta$ between the strings. When suspended in a liquid of density $\sigma$,the angle $\theta$ remains the same. The dielectric constant $K$ of the liquid is

This question contains Statement-$1$ and Statement-$2$. Of the four choices given after the statements,choose the one that best describes the two statements.
Statement-$1$ : For a charged particle moving from point $P$ to point $Q$,the net work done by an electrostatic field on the particle is independent of the path connecting point $P$ to point $Q$.
Statement-$2$ : The net work done by a conservative force on an object moving along a closed loop is zero.

Four point charges,each of $+q$,are rigidly fixed at the four corners of a square planar soap film of side $a$. The surface tension of the soap film is $\gamma$. The system of charges and the planar film are in equilibrium,and $a = k \left[ \frac{q^2}{\gamma} \right]^{1/N}$,where $k$ is a constant. Then $N$ is: